Unit 6
MHF 4U1
Lesson 6– Solving Quadratic Trigonometric Equations
Quadratic Trigonometric Equations are ones that involve the square of a trig ratio.
This leads to a quadratic trigonometric equation that can be solved algebraically or
graphically.
To solve quadratic trigonometric trig equations you may need to use one or all of
the following methods:



Factor the equation and then solve for each factor.
If factoring does not work, you may need to use the quadratic formula.
You may need to use the Pythagorean identity, compound angle formula, or
double angle formula to create a quadratic equation that contains only a
single trig function.
Example 1: Factor each of the following trig expressions.
a) cos 2   cos 
b) sin 2   2 sin   1
c) 25 tan 2 x  100
d) 2 sin 2 x  5 sin x  3
Example 1: Solve each equation in the interval 0  x  2 .
a) sin 2 x  sin x  2
Unit 6
b) 2 sin 2 x  3 sin x  1  0
c) 2 sec 2 x  3  tan x  0
d) 3sin x  3 cos 2x  2
MHF 4U1